The illumination problem is a resolved mathematical problem first posed by Ernst Straus in the 1950s.[1] Straus asked if a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking if a billiard table can be constructed in any required shape, such that there is a point where it is impossible to <dfn style="border-bottom:1px dotted #0645AD; font-style:inherit;">pot</dfn> the billiard ball in a <dfn style="border-bottom:1px dotted #0645AD; font-style:inherit;">pocket</dfn> at another point, assuming the ball continues infinitely rather than stopping due to friction.
The problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room.[1] Using the properties of the ellipse, he showed there exists a room with curved walls that must always have dark regions if lit only by a single point source. This was a borderline case, however, since a finite number of dark points (rather than regions) are not illuminable from any given position of the point source. An improved solution was put forward by D. Castro in 1997, with a 24-sided room with the same properties.[1]